Hall conductivity phase transitions and the relevance of spin-orbit interaction in a 2D electron gas subject to inhomogeneous magnetic fields

We show numerical and analytical results for a 2D electron gas in an inhomogeneous magnetic field including Zeeman and spin-orbit interaction. Radially distorted Landau levels can be identified as well as magnetic field induced density and current oscillations close to the magnetic impurity. Eventually, the distorted Landau levels give rise to negative and positive Hall conductivity phases, with sharp transitions at specific Fermi energies.¹ Furthermore, the inclusion of the spin-orbit interaction gives rise to a quantization of the many-body Berry phase in a non-meromorphic setting for adiabatic magnetic field variations. In addition, analytic results become feasible even for certain non-adiabatic cases.